What is the Greatest Common Factor of 32200 and 32210?

Greatest common factor (GCF) of 32200 and 32210 is 10.

GCF(32200,32210) = 10

We will now calculate the prime factors of 32200 and 32210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32200 and 32210.

How to find the GCF of 32200 and 32210?

We will first find the prime factorization of 32200 and 32210. After we will calculate the factors of 32200 and 32210 and find the biggest common factor number .

Step-1: Prime Factorization of 32200

Prime factors of 32200 are 2, 5, 7, 23. Prime factorization of 32200 in exponential form is:

32200 = 2³ × 5² × 7¹ × 23¹

Step-2: Prime Factorization of 32210

Prime factors of 32210 are 2, 5, 3221. Prime factorization of 32210 in exponential form is:

32210 = 2¹ × 5¹ × 3221¹

Step-3: Factors of 32200

List of positive integer factors of 32200 that divides 32200 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 23, 25, 28, 35, 40, 46, 50, 56, 70, 92, 100, 115, 140, 161, 175, 184, 200, 230, 280, 322, 350, 460, 575, 644, 700, 805, 920, 1150, 1288, 1400, 1610, 2300, 3220, 4025, 4600, 6440, 8050, 16100

Step-4: Factors of 32210

List of positive integer factors of 32210 that divides 32200 without a remainder.

1, 2, 5, 10, 3221, 6442, 16105

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32200 and 32210. The biggest common factor number is the GCF number.
So the greatest common factor 32200 and 32210 is 10.

Also check out the Least Common Multiple of 32200 and 32210